Recent questions tagged sec-b

Evaluate $ \begin{vmatrix} cos\alpha \; cos\beta & cos\alpha \; sin\beta & -sin\alpha \\ -sin\beta & cos\beta & 0 \\ sin \alpha \; cos\beta & sin\alpha \; sin\beta & cos\alpha \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Without expanding the determinant, prove that $ \begin{vmatrix} a &a^2 &bc \\ b &b^2 &ca \\ c &c^2 &ab \end{vmatrix}\; = \; \begin{vmatrix} 1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{Prove that the determinant } \begin{vmatrix} x&sin\theta&cos\theta \\ -sin\theta&-x&1\\ cos\theta&1&x \end{vmatrix} \text{ is independent of } \theta \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: $5x+2y=3$ $3x+2y=5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: $4x-3y=3$ $3x-5y=7$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: $2x-y=-2$ $3x+4y = 3$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: $5x+2y=4 $ $7x+3y = 5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Form the differential equation representing the family of curves given by $(x-a)^2+2y^2\;=\;a^2$, where $a$ is an arbitrary constant

asked Nov 29, 2012 by sreemathi.v

1 answer

prove that \[tan^{-1} \left ( \frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{{\sqrt {1+x}}+{\sqrt {1-x}}} \right ) = \frac {\pi}{4} -\frac{1}{2} cos^{-1}x,-\frac{1}{\sqrt2} \leq x \leq 1 \]

asked Nov 29, 2012 by vaishali.a

1 answer

\[ \text{For the matrix A = } \begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}, \text{ find the numbers a and b such that } A^{2} + aA + bI = O \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that \[cot^{-1} \left ( \frac {{\sqrt {1+sinx}}+{\sqrt {1-sinx}}}{{\sqrt {1+sinx}}-{\sqrt {1-sinx}}} \right ) = \frac {x}{2} , x \in \left ( 0, \frac{\pi}{4} \right )\]

asked Nov 29, 2012 by vaishali.a

1 answer

Prove that \[\frac{9 \pi}{8} - \frac{9}{4} sin ^{-1}\frac{1}{3}= \frac{9}{4} sin^{-1}\frac{2\sqrt 2}{3}\]

asked Nov 29, 2012 by vaishali.a

1 answer

Find the inverse of the matrix (if it exists): \[ \begin{bmatrix} 1&0&0 \\ 0&cos\alpha&sin\alpha \\ 0&sin\alpha&-cos\alpha \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following \[2tan^{-1} (cos x) = tan^{-1} (2\, cosec\, x) \]

asked Nov 29, 2012 by vaishali.a

1 answer

Solve the following $tan^{-1} \frac{1-x}{1+x} =\frac{1}{2} tan^{-1} x,(x>0)$

asked Nov 29, 2012 by vaishali.a

2 answers

Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2 & 1& 3 \\ 4 &- 1 & 0 \\ -7 & 2 & 1 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1 \\ \end{bmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 1&2&3 \\ 0&2&4 \\ 0&0&5 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 2&3 \\ - 4&-6 \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Choose the correct answer. If $\sin^{-1}(1-x) -2 \sin^{-1} x=\large\frac {\pi}{2}, $ then $x$ is equal to

asked Nov 28, 2012 by vaishali.a

1 answer

What is the value of: \[tan^{-1} \bigg( \frac {x}{y} \bigg) -tan^{-1} \frac {x-y}{x+y} \]

asked Nov 28, 2012 by vaishali.a

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} a^2+1&ab&ac \\ ab&b^2+1&bc \\ ca&cb&c^2+1 \end{vmatrix} = 1+a^2+b^2+c^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1+a^2-b^2&2ab&-2b \\ 2ab&1-a^2+b^2&2a \\ 2b&-2a&1-a^2-b^2 \end{vmatrix} = (1+a^2+b^2)^3 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1&x&x^2 \\ x^2&1&x \\ x&x^2&1 \end{vmatrix} = (1-x^3)^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that $ (i) \begin{vmatrix} a-b-c&2a&2a \\ 2b&b-c-a&2b \\ 2c&2c&c-a-b \end{vmatrix} = (a+b+c)^3 $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that $ (i) \begin{vmatrix} x+4&2x&2x \\ 2x&x+4&2x \\ 2x&2x&x+4 \end{vmatrix} = (5x+4)(4-x)^2 $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[\begin{vmatrix} x&x^2&yz \\ y&y^2&zx \\ z&z^2&xy \end{vmatrix} = (x-y)(y-z)(z-x)(xy+yz+zx) \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that $ (i) \quad \begin{vmatrix} 1&a&a^2 \\ 1&b&b^2 \\ 1&c&c^2 \end{vmatrix} = (a-b)(b-c)(c-a) $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} -a^2&ab&ac \\ ba&-b^2&bc \\ ca&cb&-c^2 \end{vmatrix} = 4a^2b^2c^2\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the value of the following:\[cos^{-1} \frac {1} {2} +2 sin^{-1}\frac {1} {2} \]

asked Nov 28, 2012 by vaishali.a

2 answers